Evaluate cot0 if sin0= square root of 6/5

To evaluate cot θ given that sinθ=√6/5 we shall have:
sin θ=opposite/hypotenuse
hence
opposite=√6
hypotenuse=5
thus the adjacent will be found using the Pythagorean theorem
c²=a²+b²
plugging in the value we get:
5²=(√6)²+b²
b²=25-6
b²=19
b=√19
thus
adjacent=√19
but
cotθ=1/tanθ
tanθ=√6/√19
hence:
cotθ=√19/√6